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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 87 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1984.1.e.a	$1984$	$1$	1984.e	31.b	$2$	$1$	$1$	$0.990$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+q^{5}-q^{7}+q^{9}+q^{19}+q^{31}-q^{35}+\cdots$
1984.1.e.b	$1984$	$1$	1984.e	31.b	$2$	$1$	$1$	$0.990$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$1$		$1$		$q+q^{5}+q^{7}+q^{9}-q^{19}-q^{31}+q^{35}+\cdots$
1984.1.j.a	$1984$	$1$	1984.j	496.j	$4$	$2$	$1$	$0.990$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(1-i)q^{5}-iq^{7}+iq^{9}+(1+i)q^{19}+\cdots$
1984.1.j.b	$1984$	$1$	1984.j	496.j	$4$	$4$	$2$	$0.990$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$2$		$q+(\zeta_{12}^{4}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{9}+\cdots$
1984.1.q.a	$1984$	$1$	1984.q	248.m	$6$	$4$	$2$	$0.990$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{11}+\cdots$
1984.1.q.b	$1984$	$1$	1984.q	248.m	$6$	$4$	$2$	$0.990$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}-\zeta_{12}^{4}q^{11}+\cdots$
1984.1.s.a	$1984$	$1$	1984.s	124.i	$6$	$4$	$2$	$0.990$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}+\cdots$
1984.1.bf.a	$1984$	$1$	1984.bf	124.l	$10$	$8$	$2$	$0.990$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{20}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{5}-\zeta_{20}^{3}q^{7}+\cdots$
1984.1.bn.a	$1984$	$1$	1984.bn	1984.an	$16$	$8$	$1$	$0.990$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$-8$	$0$		$1$		$q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-1-\zeta_{16}+\cdots)q^{5}+\cdots$
1984.1.bn.b	$1984$	$1$	1984.bn	1984.an	$16$	$16$	$2$	$0.990$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$8$	$0$		$1$		$q+\zeta_{48}^{14}q^{2}-\zeta_{48}^{4}q^{4}+(-\zeta_{48}^{16}+\cdots)q^{5}+\cdots$
1984.2.a.a	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
1984.2.a.b	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+3q^{7}+q^{9}-2q^{11}+\cdots$
1984.2.a.c	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{5}+q^{7}+q^{9}-6q^{11}+\cdots$
1984.2.a.d	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}-3q^{9}+6q^{11}+4q^{13}+\cdots$
1984.2.a.e	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-3q^{9}-6q^{11}+4q^{13}+\cdots$
1984.2.a.f	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}-2q^{13}-6q^{17}-4q^{19}+\cdots$
1984.2.a.g	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}-2q^{13}-6q^{17}+4q^{19}+\cdots$
1984.2.a.h	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-3q^{7}-3q^{9}-2q^{11}+4q^{13}+\cdots$
1984.2.a.i	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+3q^{7}-3q^{9}+2q^{11}+4q^{13}+\cdots$
1984.2.a.j	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots$
1984.2.a.k	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-3q^{7}+q^{9}+2q^{11}+\cdots$
1984.2.a.l	$1984$	$2$	1984.a	1.a	$1$	$1$	$1$	$15.842$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}-q^{7}+q^{9}+6q^{11}+\cdots$
1984.2.a.m	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
1984.2.a.n	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-q^{5}+(2-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
1984.2.a.o	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots$
1984.2.a.p	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(-1+\beta )q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots$
1984.2.a.q	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(1+\beta )q^{7}-q^{9}+(2-2\beta )q^{11}+\cdots$
1984.2.a.r	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(-2+\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
1984.2.a.s	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2\beta q^{5}-2q^{7}+(1+2\beta )q^{9}+\cdots$
1984.2.a.t	$1984$	$2$	1984.a	1.a	$1$	$2$	$2$	$15.842$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$4$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+(-2+\beta )q^{5}-\beta q^{7}+q^{9}+\cdots$
1984.2.a.u	$1984$	$2$	1984.a	1.a	$1$	$3$	$3$	$15.842$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots$
1984.2.a.v	$1984$	$2$	1984.a	1.a	$1$	$3$	$3$	$15.842$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(1-\beta _{2})q^{5}+\cdots$
1984.2.a.w	$1984$	$2$	1984.a	1.a	$1$	$3$	$3$	$15.842$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{3}-\beta _{2}q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots$
1984.2.a.x	$1984$	$2$	1984.a	1.a	$1$	$3$	$3$	$15.842$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
1984.2.a.y	$1984$	$2$	1984.a	1.a	$1$	$4$	$4$	$15.842$	4.4.13968.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots$
1984.2.a.z	$1984$	$2$	1984.a	1.a	$1$	$4$	$4$	$15.842$	4.4.13968.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
1984.2.a.ba	$1984$	$2$	1984.a	1.a	$1$	$6$	$6$	$15.842$	6.6.66862976.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
1984.2.a.bb	$1984$	$2$	1984.a	1.a	$1$	$6$	$6$	$15.842$	6.6.66862976.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
1984.2.b.a	$1984$	$2$	1984.b	248.b	$2$	$8$	$8$	$15.842$	8.0.3317760000.4	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+q^{9}+2\beta _{5}q^{11}+\cdots$
1984.2.b.b	$1984$	$2$	1984.b	248.b	$2$	$16$	$16$	$15.842$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-62}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{22}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{5}q^{3}-\beta _{3}q^{7}+(-3+\beta _{8})q^{9}-\beta _{2}q^{11}+\cdots$
1984.2.b.c	$1984$	$2$	1984.b	248.b	$2$	$40$	$40$	$15.842$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1984.2.c.a	$1984$	$2$	1984.c	8.b	$2$	$4$	$4$	$15.842$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{3}-2\zeta_{8}^{2}q^{5}+(-2-\zeta_{8}^{3})q^{7}+\cdots$
1984.2.c.b	$1984$	$2$	1984.c	8.b	$2$	$4$	$4$	$15.842$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{3}+2\zeta_{8}^{2}q^{5}+(2+\zeta_{8}^{3})q^{7}+\cdots$
1984.2.c.c	$1984$	$2$	1984.c	8.b	$2$	$6$	$6$	$15.842$	6.0.3182656.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(\beta _{4}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1984.2.c.d	$1984$	$2$	1984.c	8.b	$2$	$6$	$6$	$15.842$	6.0.3182656.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
1984.2.c.e	$1984$	$2$	1984.c	8.b	$2$	$20$	$20$	$15.842$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{15}q^{5}+\beta _{6}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1984.2.c.f	$1984$	$2$	1984.c	8.b	$2$	$20$	$20$	$15.842$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{15}q^{5}-\beta _{6}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1984.2.h.a	$1984$	$2$	1984.h	124.d	$2$	$2$	$2$	$15.842$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-4$	$-6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}-3q^{5}+\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{13}+\cdots$
1984.2.h.b	$1984$	$2$	1984.h	124.d	$2$	$2$	$2$	$15.842$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$-6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{3}-3q^{5}-\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{13}+\cdots$
1984.2.h.c	$1984$	$2$	1984.h	124.d	$2$	$4$	$4$	$15.842$	$\Q(\sqrt{2}, \sqrt{-13})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}-q^{9}+2\beta _{1}q^{11}+\cdots$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.